Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Trim the Brussels sprouts and cut them in half; peel the carrots and slice them into 1/2-inch rounds; roughly chop the red onion.
In a large bowl, toss the Brussels sprouts, carrots, and red onion with 0.5 tbsp of olive oil and half of the sea salt and black pepper.
Spread the vegetables in a single layer on the prepared baking sheet and roast for 20-25 minutes until tender and slightly caramelized.
While the vegetables roast, season the chicken breast evenly on both sides with the dried oregano and the remaining sea salt and black pepper.
Heat the remaining 0.5 tbsp of olive oil in a stainless steel or cast iron skillet over medium-high heat.
Place the chicken in the skillet and sear for 6-7 minutes per side, or until the internal temperature reaches 165°F and the exterior is golden brown.
In the final minute of cooking the chicken, add the minced garlic to the pan, stirring it around the chicken until fragrant but not burnt.
Remove the chicken from the heat and let it rest for 3 minutes before serving alongside the roasted vegetables.